Finally, we will now present simulations of the flow inside a square cavity driven by the shear from the motion of the top lid. It is a standard flow problem for benchmarking new CFD methods by going beyond the use of analytical solutions and involves flow patterns characterized by the presence of a main or primary vortex around center of the cavity and accompanied by various secondary vortices around the corners, whose sizes and locations depend on the Reynolds number \(\mbox{Re}\) . Prior rectangular LB schemes based on either SRT or orthogonal MRT formulations have been used to perform simulations of this problem [1]}, [2]}, [3]}, [4]}, [5]}, which have reported results for only relatively low \(\mbox{Re}\)  as they were often subjected to numerical instability issues when the Reynolds number was increased to even moderate values. Hence, it would be interesting to study the performance of the present RNR-LBM and RC-LBM for this case study. For a square cavity of side \(H\)  whose top lid is set into a uniform motion at a velocity \(U\) , the characteristic Reynolds number can be defined as \(\mbox{Re}=UH/\nu \) . We carried out simulations of this flow problem using both RNR-LBM and RC-LBM involving rectangular lattices with grid aspect ratios of \(a=4, 2, 0.8, 0.5, 0.25\) , and \(0.2\)  at a wide range of Reynolds numbers of 100, 400, 3200, 5000 and 7500 covering those reported in a prior work providing benchmark numerical solutions based on a NS solver [6]}. The choices of the various parameters considered for these simulations are given in Table REF . The half-way bounce back scheme was used to impose the no-slip conditions on all the bounding walls, with momentum correction being added to those for the top wall via Eqs. (REF )-() constructed for use with the rectangular lattice.
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